I am seeing an unusual sporadic failure of one of our patches at several customer sites. The final error code is 1648 (No valid sequence could be found for the set of patches),
It really sounds like you are using patches effectively, but you are definitely breaking my number one rule for a patch: it should be smaller than its base MSI.
The reason is plain and simply that a patch is just a delivery mechanism for an update that is already working. As such it is just a container that is more complicated and error prone than the original setup itself, and when its size exceeds the original MSI there is no obvious reason to use the patch at all? You can just run the full setup without modification? In fact you should try exactly that on the systems where the problem occurs.
Maybe I am missing something important? Perhaps it installs faster? A well authored minor upgrade, or a major upgrade that doesn't uninstall and reinstall but just unregisters the older version (late sequencing for RemoveExistingProducts) should be just as fast.
Despite years of experience and deployment expertise, I am no patching expert. I actively try to minimize patch use, since it is generally more trouble than it is worth. But here is a post with some of my patching experiences.
I apologize if this seems like no answer at all, but I feel this is a valid input since your patch seems so unnecessary at 57MB, and you are bound to have a workaround already: the full update MSI.